Middle school math problems. Use inequalities to solve, junior high school inequality solving method

Let's say there are x boxes, y parts.

Get the inequality.

y=5x+1 ①

6(x-2)≤y<6(x-1) ②

Substitute to get.

6(x-2)≤5x+1<6(x-1)

6x-12≤5x+1<6x-6

7 then x = 8, 9, 10, 11, 12

y = 41, 46, 51, 56, 61 respectively

There are six sets of solutions so there are at least 8 boxes with 41 parts.

Solution: If there are x chests, there are parts (5x+1).

5x+1≤6（x-1) (1)

5x+1≥6（x-2) (2）

From (1): x 7

From (2): x 13

7≤x ≤13

x=7 (discarded if not on topic).

So at least 8 boxes, 41 parts.

Solution: If there are x boxes, there are (5x+1) parts, which is derived from the title.

0<(5x+1)-6(x-2)<6

Solve 7 because the smallest integer value of x is 8, so there are at least 8 chests, and when x = 8, 5x + 1 = 41

A: At least 8 boxes, 41 parts.

Let's say there are x chests, you can get it.

6（x-2）＜5x+1＜6（x-1）

It's OK to solve it yourself.

5x+1 is the number of parts.

With x boxes, there are y parts, then.

y=5x+1

6*(x-2) is fine.

The methods and techniques for solving inequalities in junior high school are as follows:

Solve absolute value problems (simplification, evaluation, equations, inequalities, functions) and transform problems with absolute values into problems without absolute values. The specific conversion methods are:

1) Classification discussion method: remove the absolute value according to the positive, zero and negative fractions of the number or formula in the absolute value symbol.

2) Zero-point segmentation discussion method: It is suitable for the case of multiple absolute values containing one letter to clear the reed.

3) Two-sided flat method: suitable for equations or inequalities that are non-negative on both sides.

4) Geometric meaning method: It is suitable for situations with obvious geometric significance.

The undetermined coefficient method is a method of finding an object under the condition that the form of the object is known. It is suitable for solving important scattered chain problems such as finding the coordinates of points, analytic formulas of functions, and curve equations.

The concept of inequality is as follows:

Generally speaking, the formula that expresses the size relationship with the pure greater than sign ">" and less than the sign "<" is called an inequality. The formula that uses "≠" to represent an inequality relationship is also an inequality.

The common domain of the analytic formula on both sides is called the domain of the inequality.

Integer inequality:

Integer inequalities are integers on both sides (i.e., unknowns are not on the denominator).

Unary Inequalities: Inequalities that contain one unknown number (i.e., unary number) and the number of unknowns is one (i.e., one). Such as 3-x>0

In the same way, a binary inequality is an inequality that contains two unknowns (i.e., binary) and the number of unknowns is one (i.e., one).

,x＞a

1-x＞0,x＜1

x has three integer solutions, i.e., x=0, -1, -2, so -3 a -2

Multiply 8,24-2x-2 at the same time 16-3+3x

22-2x≥13+3x

5x≥-9x≤9/5

Multiply 6, 6x+30-2x+2, 6x+9+2x-14x+32, 8x+8

4x＞-24

Solution: x+2 The set of solutions for 0 is: x -2

x-1) The solution set for 2+1 x is: x 1

So the solution set of the original inequality is: -2 x 1

The Mathematics Q&A team will answer for you, I hope it will be helpful to you.

x -2, x 1, hence: -2 x 1

Figure: -2 solid, 1 hollow, and wired.

I wish you progress in your studies and go to the next level! (

The above inequality is solved as x>=-2

The inequality below x-1>2(x-1) x<1

In summary, -2< = x<1

Solve inequality (1) x>=-2Inequality (2) x<1, then find the common part, -2<=x<1, and then on the number line, the point of -2 is solid, and the point of 1 is hollow, and the connection is the set of solutions obtained.

-2 x 1 is a real point at -2 on the number line, and 1 out is an imaginary point.

The answer should be t<0 or t>6

Sub-situation: In the first case, t<0 is directly established.

Second, when t>0, first multiply both sides by 4 at the same time to get 12 2t<1, and after about minutes, we get 6 t<1

Then multiply both sides by t at the same time to get t>6